Thermodynamics and phase transition of Bardeen–AdS-class black holes

In a generalized parameter space, regular black holes can be regarded as non-singular solutions under specific parameters in Einstein gravity theory coupled with non-linear electromagnetic fields. Following this concept, we investigate the thermodynamic states and phase transitions of Bardeen–AdS-class black holes, revealing that the system can be classified into two categories, Type I and Type II, based on whether it adopts a pure Bardeen–AdS spacetime without event horizons or a Bardeen–AdS black hole as its phase state, each exhibiting distinct thermodynamic properties. If one includes the Bardeen–AdS black holes in the system (Type I), there will be three distinct black hole states and the phase transitions between them are analogous to the Reissner–Nordstrom–AdS black holes. On the other hand, if the pure Bardeen–AdS spacetime is included (Type II), an additional tiny black hole state emerges. A phase transition reminiscent of the Hawking–Page transition was found. Significantly, in this scenario, thermodynamical characteristic curves exhibit discontinuous behavior, which attributes to the multiple horizons. The presence of a Bardeen–AdS black hole within the phase structure of the Bardeen–AdS-class black hole profoundly modifies the thermodynamical properties of the system, highlighting the novel aspects of regular black holes.